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We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…
Recently, neural networks have been widely applied in the power system area. They can be used for better predicting input information and modeling system performance with increased accuracy. In some applications such as battery degradation…
This paper proposes a Perturbed Proximal Gradient ADMM (PPG-ADMM) framework for solving general nonconvex composite optimization problems, where the objective function consists of a smooth nonconvex term and a nonsmooth weakly convex term…
Finding the stationary states of a free energy functional is an important problem in phase field crystal (PFC) models. Many efforts have been devoted for designing numerical schemes with energy dissipation and mass conservation properties.…
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified…
Multi-way data arises in many applications such as electroencephalography (EEG) classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit…
The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…
To enhance the nonlinearity of neural networks and increase their mapping abilities between the inputs and response variables, activation functions play a crucial role to model more complex relationships and patterns in the data. In this…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
Feed-forward ReLU neural networks partition their input domain into finitely many "affine regions" of constant neuron activation pattern and affine behaviour. We analyze their mathematical structure and provide algorithmic primitives for an…
This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of…
To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. The objective of this research work is to extend this method…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to…